Dawn has recently revealed that the surface of Vesta is heterogeneously covered by polymictic regoliths represented by mixtures of howardite, eucrite, and diogenite (HED) meteorites. Mixing relations of the HED suite are examined here using a new computational statistical approach of independent component analysis (ICA). We performed eight-component ICA (Si, Ti, Al, Cr, Fe, Mn, Mg, and Ca) for 209 HED bulk-rock compositions. The ICA results indicate that the HED bulk-rock compositions can be reduced into three independent components (IC) and these IC vectors can reasonably explain compositional variation, petrographic observations, and the mixing relations of the HED suite. The IC-1 vector represents a eucrite variation that extends from cumulate eucrite toward main-group (MG) and incompatible-element enriched eucrites. The IC-2 vector represents a compositional variation of howardites that extends from diogenites to MG-eucrites, indicating the well-known two-component mixing trend of diogenite and eucrite. The IC-3 vector represents a compositional variation defined by diogenites and olivine-bearing diogenites, suggesting mixing of olivine and orthopyroxene. Among the three ICs, the diogenite-eucrite mixing trend IC-2 is most statistically robust and dominates the compositional variations of the HED suite. Our ICA study further indicates that the combination of only three elements (Mg, Si, and Fe) approximates the eight-component ICA model, and that the limited number of resolvable γ-ray spectra obtained by the Dawn mission possibly discriminates olivine lithologies from the olivine-free regolith breccias on the surface of Vesta.